Bio
I am a Phillip Griffiths Assistant Research Professor at Duke University. Previously, I was a postdoc researcher (July 2021- July 2022) at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany.
I received my Ph.D. at Stanford University under the supervision of Lenya Ryzhik and Lexing Ying (2016-2021). Before that I was an undergraduate student at University of California, Los Angeles (2012-2016).
Research Interests
I am broadly interested in the mathematical aspects of machine learning and data science problems,
using tools from stochastic analysis and partial differential equations. I also study evolution equations including reaction diffusion equations.
Papers
- Why does the
two-timescale Q-learning converge to different mean field solutions? A
unified convergence analysis, with Jianfeng Lu, Yue Wu, and Yang Xiang. Submitted [arXiv]
- Convergence of stochastic gradient de-
scent under a local Lojasiewicz condition for deep neural networks, with Jianfeng Lu. Submitted [arXiv]
- Front location
determines convergence rate to traveling waves, with Christopher Henderson and Lenya Ryzhik. Annales de l'Institut Henri Poincaré C [link]
- Critical points and convergence analysis of generative deep linear net-
works trained with Bures-Wasserstein loss, with Pierre Brechet, Katerina Papagiannouli, and Guido Montufar. ICML [link]
- Voting models
and semilinear parabolic equations, with Christopher Henderson and Lenya Ryzhik. Nonlinearity [link]
- Quantitative
steepness, semi-FKPP reactions, and pushmi-pullyu fronts, with Christopher Henderson and Lenya Ryzhik. Arch. Ration. Mech. Anal [link]
- Pushed, pulled and pushmi-pullyu fronts of the
Burgers-FKPP equation, with Christopher Henderson and Lenya Ryzhik. J. Eur. Math. Soc. [link]
- Combining resampling and reweighting
for faithful stochastic optimization, with Lexing Ying. Comm. Math. Sci. [link]
- Why resampling outperforms
reweighting for correcting sampling bias with stochastic gradients, with Lexing Ying and Yuhua Zhu. ICLR [link]
- On the gradient flow structure of the
isotropic Landau equation, with Lexing Ying. Comm. Math. Sci. [link]
- Global well-posedness for the Euler
alignment system with mildly singular interactions, with Lenya Ryzhik. Nonlinearity [link]
- Stochastic modified equa-
tions for the asynchronous stochastic gradient descent, with Jianfeng Lu and Lexing Ying. Information
and Inference: A Journal of the IMA [link]
- Fast algorithms for integral
formulations of steady-state radiative transfer equation, with Yuwei Fan and Lexing Ying. Journal of
Computational Physics [link]
- Image segmentation
with dynamic artifacts detection and bias correction, with D. Zosso, J. Stevick, N. Takaki, M. Weiss, L. S. Slaughter,
H. H. Cao, P. S. Weiss, and A. L. Bertozzi. AIMS Inverse
Problems and Imaging [link]
Teaching
I am teaching Math 356: Elementary Differential Equations in Fall 2024 Canvas page